Set \( h(t) = 0 \): \( -5t^2 + 20t + 45 = 0 \)
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- \( a_{10} = 350 - 288 = 62 \)
- #### 10th term: 62
- A ball is thrown upward from a 45-meter tall building with initial velocity 20 m/s. Its height is modeled by \( h(t) = -5t^2 + 20t + 45 \). When does it hit the ground?
- Divide by -5: \( t^2 - 4t - 9 = 0 \)
- Use quadratic formula: \( t = \frac{4 \pm \sqrt{16 + 36}}{2} = \frac{4 \pm \sqrt{52}}{2} = \frac{4 \pm 2\sqrt{13}}{2} = 2 \pm \sqrt{13} \)
- Only positive root: \( t = 2 + \sqrt{13} \approx 5.605 \) seconds
